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Operations Research 2: Advanced Operations Research (OR2)
Provider: Faculty of Science

Activity no.: 5563-21-07-31There are 49 available seats 
Enrollment deadline: 22/11/2021
PlaceDepartment of Mathematical Sciences
Universitetsparken 5, 2100 København Ø
Date and time22.11.2021, at: 08:00 - 30.01.2022, at: 16:00
Regular seats50
ECTS credits7.50
Contact personNina Weisse    E-mail address: weisse@math.ku.dk
Enrolment Handling/Course OrganiserTrine Krogh Boomsma    E-mail address: trine@math.ku.dk
Written languageEnglish
Teaching languageEnglish
Semester/BlockBlock 2
Scheme groupC
Exam formOral examination
Grading scale7 point grading scale. For PhD students: Passed / Not Passed
Course workload
Course workload categoryHours
Theory exercises28.00
Project work30.00


A. Problem formulation and modeling:
A1. Formulate mathematical optimization models for classical OR problems.
A2. Linearization of non-linear constraints.
A3. Quality of different model formulations.
A4. Modeling practical OR problems.

B. Integer Programming:
B1. Integer Programs (IP), Binary Integer Programs (BIP), and Mixed-Integer Programs (MIP).
B2. Properties of Integer Programs.
B3. Examples of Integer and Mixed-Integer Programs.

C. Solution methods for Integer Programming Problems:
C1. Relaxation and duality.
C2. Decomposition.
C3. Branch and bound.
C4. Dynamic programming.
C5. Cutting planes.
C6. Column generation.

D. Practical aspects:
D1. External talks: Relation between academia and practice.
D2. Case studies: Energy planning/Vehicle routing/Travelling salesman.
D3. Implementation of a given problem using an appropriate software package.
D4. Implementation of a solution method for a given problem.

Learning outcome
- Mathematical optimization problems, including LP, IP, BIP and MIP; classical problems such as Travelling Salesman, Knapsack and Network Flow problems.
- Properties of Integer Programming problems
- Solution methods for Integer Programming Problems

- Characterize different classes of mathematical optimization problems, including LP, IP, BIP and MIP problems
- Formulate models for LP, IP, BIP and MIP problems
- Implement a given problem using appropriate software
- Apply the solutions methods presented in the course
- Implement a solution method for a given problem (in a simplified fashion)
- Understand and reproduce the proofs presented in the course

- Evaluate the quality of different model formulations
- Discuss the challenges of solving IP problems
- Explain how to exploit the properties of a given class of IP problems in the design of a solution method
- Adapt a solution method to a given class of IP problems
- Describe similarities and differences between solution methods
- Discuss the challenges of modeling and solving practical problems
- Formulate, implement and solve a practical problem and justify the choice of model formulation and solution method

Previous years, the textbook L. A. Wolsey: Integer Programming, 1998, John Wiley & Sons, Inc. was used.

Teaching and learning methods
2 x 2 hours of lectures and 2 x 2 hours exercises/project work per week for 7 weeks.

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